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If the apex angle () and leg lengths () of an isosceles triangle are known, then the area of that triangle is: [20] T = 1 2 a 2 sin θ . {\displaystyle T={\frac {1}{2}}a^{2}\sin \theta .} This is a special case of the general formula for the area of a triangle as half the product of two sides times the sine of the included angle.
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]
The term apex may used in different contexts: In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side. [1] Here the point A is the apex. In a pyramid or cone, the apex is the vertex at the "top" (opposite the base). In a pyramid, the vertex is the point that is part of all the ...
The angle bisector of the golden triangle subdivides the side that it meets in the golden ratio, and the areas of the two subdivided pieces are also in the golden ratio. [47] If the apex angle of the golden gnomon is trisected, the trisector again subdivides it into a smaller golden gnomon and a golden triangle. The trisector subdivides the ...
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
Inside each isosceles triangle the pair of base angles are equal to each other, and are half of 180° minus the apex angle at the circle's center. Adding up these isosceles base angles yields the theorem, namely that the inscribed angle, ψ, is half the central angle, θ.
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A pyramid is a polyhedron that may be formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form an isosceles triangle called a lateral face. [7] The edges connected from the polygonal base's vertices to the apex are called lateral edges. [8]